A projectile is projected from the level ground in vertical x-y plane (vertical is y axis). The point of projection is considered as the origin. For which of the following initial velocities of projection u and angle of projection $θ$ with the horizontal will the projectile pass through the point (4, 2) (all in m) (Neglect air friction)

u = 4 \sqrt{5} \frac{m}{s}, θ = 45^{\circ}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

u = 4 \sqrt{5} \frac{m}{s}, θ = t a n^{- 1} (3)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

u = 2 \sqrt{5} \frac{m}{s}, θ = 45^{\circ}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

u = 8 \sqrt{5} \frac{m}{s}, θ = t a n^{- 1} (3)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct options are
A $u = 4 \sqrt{5} \frac{m}{s}, θ = 45^{\circ}$
B $u = 4 \sqrt{5} \frac{m}{s}, θ = t a n^{- 1} (3)$
$x = u_{x} t = (u c o s θ) t$
$\Rightarrow t = \frac{x}{u c o s θ}$
Also, $y = u_{y} t - \frac{1}{2} g t^{2}$
$\Rightarrow y = (u s i n θ) \frac{x}{u c o s θ} - \frac{1}{2} g {(\frac{x}{u c o s θ})}^{2}$
$\Rightarrow y = x t a n θ - \frac{g x^{2}}{2 u^{2} c o s^{2} θ}$
$(A) 2 = 4 \times 1 - \frac{1}{2} \frac{10 \times 4^{2}}{16 \times 5 \times \frac{1}{2}}$
$(B) 2 = 4 \times 3 - \frac{1}{2} \frac{10 \times 4^{2}}{16 \times 5 \times \frac{1}{10}}$
$(C) 2 = 4 \times 1 - \frac{1}{2} \frac{10 \times 4^{2}}{4 \times 5 \times \frac{1}{2}}$
$(D) 2 = 4 \times 3 - \frac{1}{2} \frac{10 \times 4^{2}}{64 \times 5 \times \frac{1}{10}}$

Suggest Corrections

Similar questions

Q. A projectile is projected from the level ground in vertical x-y plane (vertical is y axis). The point of projection is considered as the origin. For which of the following initial velocities of projection u and angle of projection

θ

with the horizontal will the projectile pass through the point (4, 2) (all in m) (Neglect air friction)

Take the z axis as vertical and the xy plane as horizontal. A particle A is projected at $4 \sqrt{2}$ m/s at an angle of $45^{\circ}$ to the horizontal, in the xz plane. Particle B is projected at 5 m/s at an angle $θ = t a n^{- 1} (\frac{4}{3})$ to y axis, in the yz plane. Which of the following is not correct for the velocity of B with respect to A?